标题： 共形相关的真空引力波及其对称性 显示英文标题

标题： Conformally related vacuum gravitational waves, and their symmetries

摘要： 通过重新定义的Möbius时间构建了一个特殊的保形变换，该变换将一个真空引力波转换为另一个真空引力波。它可以将一个全局定义的真空波转变为真空三明治波，或者将引力波携带到自身。 第一种类型由线性和圆极化真空平面引力波举例说明，它置换对称性和测地线。 我们研究了具有第二类共形O(2,1)对称性的pp波，这些波似乎迄今未引起注意，它们是熟悉的反平方轮廓的各向异性推广。 受分子物理启发的一个例子被详细研究，其中粒子可以逃逸，或进行周期性运动，或落入奇点。 显示英文摘要

摘要： A special conformal transformation which carries a vacuum gravitational wave into another vacuum one is built by using M\"obius-redefined time. It can either transform a globally defined vacuum wave into a vacuum sandwich wave, or carry the gravitational wave into itself. The first type, illustrated by linearly and circularly polarized vacuum plane gravitational waves, permutes the symmetries and the geodesics. Our pp waves with conformal O(2,1) symmetry of the second type, which seem to ahve escaped attention so far, are anisotropic generalizations of the familiar inverse-square profile. An example inspired by molecular physics, for which the particle can escape, or perform periodic motion, or fall into the singularity is studied in detail.